Global concerns over the atmospheric increase in carbon dioxide have lead to the study of the sources and sinks responsible for regulating that increase, and to the conclusion that the ocean is a major sink for atmospheric carbon dioxide. One aspect of the uptake of atmospheric carbon dioxide by the oceans is the flux of carbon through the surface mixed layer into the deep ocean, controlled in part by the fixation of carbon by marine phytoplankton through the photosynthetic process of primary production. The estimation of oceanic phytoplankton biomass, and the primary production which leads to that biomass on regional and global scales, is the focus of efforts using both in situ measurements and remote sensing techniques. This paper surveys the present state of our understanding of the estimation of marine primary production by remote sensing techniques, through the modeling of the physiological mechanisms of carbon assimilation by phytoplankton, and the relationship of these techniques to in situ estimates. This model requires measurements of surface pigments and a determination of the incident solar irradiance as a measure of the energy available for photosynthesis.